Evidence for a vibrational phase isotope effect on the photochemistry of vision
C. Schnedermann1,α, X. Yang2, M. Liebel1,£, K. M. Spillane1,3,%,
J. Lugtenburg4, I. Fernandez4,$, A. Valentini5,&, I. Schapiro6, M. Olivucci2,5,7,*, P. Kukura1,*, R. A. Mathies3,*
1 Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, OX1 3QZ Oxford, United Kingdom.
2 Chemistry Department, Bowling Green State University, Bowling Green, Ohio 43403, United States.
3 Chemistry Department, University of California, Berkeley CA 94720, United States.
4 Leiden Institute of Chemistry, Leiden University, 2300 RA Leiden, The Netherlands.
5 Dipartimento di Biotecnologie, Chimica e Farmacia, Università di Siena, via A. Moro 2, I-53100 Siena, Siena, Italy.
6 Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
7 University of Strasbourg, Institute for Advanced Studies, 5, Allée du Général Rouvillois, F-67083 Strasbourg, France.
αCurrent address: Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, Massachusetts 02138, United States.
£Current address: ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science & Technology, 08860 Castelldefels (Barcelona), Spain.
%Current address: Department of Physics, King's College London, London WC2R 2LS, United Kingdom.
$Current address: IFF International Flavors and Fragrances, Avda. Felipe Klein 2, 12580 Benicarló, Spain.
&Current address: Département de Chimie, Université de Liège, Allée du 6 Août, 11, 4000 Liege, Belgium.
Abstract
Vibronic coupling is key to efficient energy flow in molecular systems and a critical component of most mechanisms invoking quantum effects in biological processes. Despite increasing evidence for coherent coupling of electronic states being mediated by vibrational motion, it is not clear how and to what degree properties associated with vibrational coherence such as phase and coupling of atomic motion can impact the efficiency of light-induced processes under natural, incoherent illumination. Here, we show that deuteration of the H11-C11=C12-H12 double-bond of the 11-cis retinal chromophore in the visual pigment rhodopsin significantly and unexpectedly alters the photoisomerization yield while inducing only small changes in the ultrafast isomerization dynamics assignable to known isotope effects. Combination of these results with non-adiabatic molecular dynamics simulations reveals a vibrational phase-dependent isotope effect that we suggest is an intrinsic attribute of vibronically coherent photochemical processes.
The breakdown of the Born-Oppenheimer approximation separating electronic and nuclear degrees of freedom forms the basis of energy flow in molecules.1,2 The conventionally proposed mechanism of rapid (<10 ps) condensed-phase photochemical processes is undergoing revision as a result of the combined efforts of modern ultrafast spectroscopic techniques and theoretical modeling. For multi-chromophoric systems such as light harvesting complexes, coherent vibronic coupling of electronic states has been suggested as a potential source of quantum effects influencing and possibly optimizing the outcome of energy transfer.3–10 Other extremely rapid photochemical processes such as the primary isomerization of the retinal chromophore in rhodopsin, are now classified as intramolecular vibrationally coherent internal conversion processes through an early conical intersection (CI) allowing for the rapid formation of isomerized photoproduct irrespective of illumination conditions.11–17 A key question that remains unanswered is whether this coherence is functionally significant.
Highly time-resolved transient grating studies of rhodopsin recently reported the sub-50 fs appearance of excited photoproduct and extracted short lifetime oscillatory vibrational features assigned to the transient excited state.18,19 These observations suggest that the vibrational motion of key modes that make up the isomerization coordinate, like the C11=C12 torsion and H-C11=C12-H hydrogen out-of-plane (HOOP) wags (also described as coupled C11 and C12 pyramidalizations) could be an important factor in determining the efficiency and outcome of the reaction. Furthermore, molecular dynamics simulations of the rhodopsin surface crossing have proposed that the phase of vibrational motions upon encountering the CI connecting the excited and ground electronic states is important for the reactivity.13–15,20–25 In particular, recent theoretical studies on the isomerization dynamics in rhodopsin have emphasized that the degree of intramolecular vibrational coherence plays a crucial role for the quantum yield of photoproduct formation.26,27 Despite multiple indications that the relative phase of vibrational modes may be important in rhodopsin photochemistry,13,25,28 there is no direct experimental evidence suggesting its relevance for the chemical outcome, in particular with biologically relevant, incoherent excitation.
An informative means to test the reactive influence of vibrational modes and their phase relationship at the CI involves isotopic labeling. Isotopes have traditionally been employed to study reaction mechanisms
through primary kinetic isotope effects where the isotopomer is transferred, such as in the light-driven proton transfer in green-fluorescent protein.29,30 The primary kinetic isotope effect arises from the change in the zero-point energy for the heavier atom, but even larger effects have been reported when tunneling plays a role in the reaction mechanism.30 In the context of visual photochemistry, early studies suggested a primary kinetic isotope effect associated with chromophore proton or hydrogen transfer, but these models have not been sustained.31,32
To examine the effect of isotopic substitution on the photochemistry of vision, we synthesized three modified 11-cis retinal analogues (11-D, 12-D and 11,12-D2) and regenerated these chromophores in the opsin protein (Fig. 1). We then characterized the isomerization quantum yield using a continuous-wave light source33–35 and the isomerization kinetics by recording the dynamic appearance of the photoproduct using ultrafast transient absorption spectroscopy.16,36 Isotopic substitution had a large effect on the photochemical quantum yield, which is dictated by the efficiency of internal conversion through the CI from the excited- state 11-cis reactant to the all-trans photoproduct. The effect of isotopic substitution on the photoisomerization kinetics was, however, less pronounced and followed the trend expected for known isotope effects. These results, coupled with non-adiabatic molecular dynamics simulations, suggest a novel isotope effect where mass-induced changes in vibrational phase and thereby mode-specific vibrational coupling alter the reaction efficiency of a vibronically coherent photochemical reaction.
Results and Discussion
Isomerization quantum yield
Native and 11,12-H2 regenerated rhodopsin exhibited statistically indistinguishable isomerization quantum yields of 0.63 (±0.01) and 0.65 (±0.01), respectively, demonstrating that retinal regeneration did not alter the system (Fig. 2). The 11,12-D2 derivative exhibited a quantum yield of 0.69 (±0.01), which is higher compared to the native and regenerated chromophore. In contrast, the 11-D and 12-D isotopomers, with just a single isotopic substitution, had substantially lower quantum yields of 0.45 (±0.01) and 0.48 (±0.01), respectively.
This surprising yield reduction in view of the increase for 11,12-D2 is statistically significant beyond
experimental error. The protonated 11-cis chromophore in solution exhibited an even lower quantum yield of 0.19 (±0.04) outside the protein pocket.37 These results evidence an anomalous isotope effect where symmetric deuteration of the isomerizing bond produces a higher isomerization quantum yield while asymmetric isotopic substitution significantly lowers the yield.
Transient absorption spectroscopy and dynamics
The differences in isomerization yield could in principle be explained by a non-trivial dependence of the reaction rate on isotopic substitution, especially given the proposed involvement of hydrogen wagging motion in the reaction.12,13,16,18,23,25 We thus recorded the appearance of the photoproduct of native rhodopsin and its isotopic derivatives using broadband transient absorption spectroscopy after excitation at the rhodopsin absorption maximum (498 nm) with a 20 fs pulse. We then followed the growth of the photoinduced absorption in the region from 545-616 nm, indicative of the formation of the primary photoproduct, for each derivative including native and 11,12-H2 regenerated rhodopsin (Fig. 3a). All traces exhibited the expected features known for rhodopsin photochemistry: an oscillatory coherent artifact near zero pump-probe delay,38 a delayed growth of the photoproduct signal that is complete by ~200 fs11,39 and weak modulations of the electronic signal for longer time delays caused by coherent nuclear motion of the photoproduct.16,17 The coherent artifacts are nearly identical for all derivatives with any variations caused by the different optical densities available for the five samples. The most prominent differences in the traces are restricted to the appearance of the vibrational coherence superimposed on the electronic signal in the 300-500 fs window, as expected for changes in vibrational frequencies caused by isotopic substitution. The overall similarity of the electronic dynamics suggested by the ultrafast appearance of the photoproduct signal continued throughout the entire probed region (500-900 nm, Supplementary Fig. 1).
To more carefully quantify the dynamics of photoproduct formation, we fitted the transients in Fig. 3a to a sum of a coherent artifact contribution and a mono-exponential decay function convolved with a Gaussian function describing formation of the photoproduct (Supplementary Figs. 2-4).40 This approach allowed us to define the time delay when pump and probe pulses arrive at the sample (t0,CA) independently of the time delay of photoproduct formation (t0,PIA). The difference (t0,PIA - t0,CA) provides an internally referenced measure
of the lag time for photoproduct formation, which can be taken as representative of the time it takes for the excited-state population to reach the CI (Fig. 3b). Furthermore, the rise time of the photoproduct formation (PIA) provides a measure of how quickly the excited state is depopulated once the CI is reached (Fig. 3c). We refer the reader to section 2 of the Supplementary Information for a more detailed analysis and discussion of the fitting procedure.
The retrieved average lag time is 150.6 ± 5.2 fs but the individual traces show subtle variations across the isotopomers (Fig. 3b). Native and 11,12-H2 regenerated rhodopsin are expected to show the same value but differ by 3.2 fs. While we cannot rule out that the reconstitution process introduces this difference, we attribute this difference to systematic errors not accounted for by our fitting model, putting a lower limit to the precision with which we can quantify differences between the isotopomers (see Supplementary Fig. 2- 4). Using the same procedure, we find that the lag time for 11,12-D2 increases by 9.1 fs. The 11-D isotopomer exhibits similar dynamics to 11,12-D2 (increase by 7.3 fs) while 12-D is indistinguishable from native rhodopsin. The retrieved average photoproduct formation rise time of 29.3 ± 3.4 fs (Fig. 3c) agrees with recent transient grating measurements on rhodopsin.18 The trend observed for the rise times differs significantly compared to the lag times observed in Fig. 3b as all isotopomers apart from 11-D show identical values within error bounds. We remark, however, that any fitting model can only yield strictly comparable parameters under the assumption that all samples were measured with the same optical density, which was not possible for 11-D (see Methods). Consequently, contributions from vibrational coherences and different signal-to-noise levels are likely to differentially affect the retrieved kinetic parameters.
Our analysis suggests a weak dependence of the photochemical dynamics upon isotopic substitution manifested in the delayed appearance (lag time) of the photoproduct formation for deuterated isotopomers relative to native rhodopsin. This delay is correlated with the degree of isotopic substitution and is expected based on mixing of the HOOP mode with the C11=C12 torsional mode whose frequency primarily determines the time it takes to reach the CI. A higher isotope mass will consequently result in a lower torsional frequency and a retardation of the reaction speed with our analysis revealing an upper bound for this retardation of
~7% for 11,12-D2 relative to the average of native and 11,12-H2 regenerated rhodopsin. Critically, the
variations in dynamic parameters (Fig. 3b, c) are small compared to changes in isomerization quantum yields which range from -30% to +8% (Fig. 2) and there appears to be no correlation between these observables (see Supplementary Fig. 5). The C11-H or C12-H HOOP motion is therefore not rate limiting for the reaction as might be expected based on a Landau-Zener-type surface tunneling mechanism.41,42 Traditional primary or secondary kinetic isotope effects including tunneling30 can be ruled out as well because the quantum yield for the 11,12-D2 derivative is higher and heavy isotope effects on the zero-point energy or on tunneling probability generally result in lower reaction rates.
These results can be understood by adopting an intramolecular vibrationally coherent picture of rhodopsin’s reactive internal conversion, which considers the nature and relative timing and phasing of the various nuclear motions within a single molecule. The extremely rapid isomerization event reduces the overall reaction coordinate in rhodopsin to critical displacements along a localized backbone torsion and a HOOP motion, with surface hopping restricted to a relatively narrow range of torsional angles around 90 degrees.13,25 A local isomerizing twist about the C11=C12 double bond is achieved through a correctly phased motion of the C10-C11=C12-C13 torsion and the corresponding anti-symmetric H-C11=C12-H torsion, related to the HOOP coordinate, at the CI. A successful isomerization reaction thus requires a cooperative effect of both vibrational degrees of freedom in a well-defined manner.
Quantum-chemical trajectory calculations
To obtain deeper insight into the phase relationship and role of these modes, we carried out non-adiabatic molecular dynamics simulations for all studied isotopomers using a multiconfigurational-QM/MM rhodopsin model featuring a computationally more affordable five double-bond chromophore (Fig. 4a).13,24 The excited- state lifetime and quantum yield of each isotopomer were computed by propagating 400 semi-classical trajectories starting with initial conditions corresponding to a room-temperature Boltzmann distribution. The simulated quantum yields paralleled the experimentally observed trend (increase for 11,12-D2, decrease for 11-D and 12-D) as well as the weaker isotope-dependent trend in the lag times in agreement with previous full-chromophore studies (Table 1).11,13
Motivated by this agreement between experiment and theory, we investigated the simulated trajectories to extract general trends for all isotopomers governing the underlying mechanisms. Upon analyzing the population decay we consistently observed an oscillatory behavior showing initially alternating ‘reactive‘
(formation of trans-photoproduct) and ‘unreactive‘ (formation of cis-reactant) waves associated with different subsets of the decaying population (Fig. 4b). The subsets corresponded to distinct phases of the torsion (α) and HOOP (δop) coordinate (Fig. 4a). It is instructive to define an effective coordinate τ = α −δ2op, which is proportional to the overlap between the π-orbitals involved in the breaking and reconstitution of the C11=C12 double bond (Fig. 4a, right hand side).13 We found that the ‘reactive‘ or ‘unreactive‘ direction is best described by considering the velocity of the angle τ at the CI, where a negative τ velocity leads to trans- photoproduct formation (Fig. 4c, orange) while a positive τ velocity results in cis-reactant formation (Fig. 4c, blue). Further examining the individual components of the τ motion revealed a similar α component in reactive and unreactive trajectories, rendering the velocity of δop (i.e. of the HOOP coordinate) the decisive factor determining the sign of the τ velocity and therefore the quantum yield of the reaction. As highlighted in Fig. 4d, reactive and unreactive trajectories approach the CI at approximately the same α velocity in both cases with α moving towards more negative values. Successful trans-photoproduct formation occurs, however, only if δop moves in the opposite direction to α, i.e. towards more positive values, to achieve a counterclockwise skeletal twisting motion (orange trajectory), while cis-reactant reformation is observed if δop moves in the same direction as α, i.e. towards more negative values (blue trajectory).
Following these findings, we can now reconcile the discrepancy arising between the modest changes in reaction rates and the non-monotonous trend in isomerization quantum yields for rhodopsin isotopomers.
Partial deuteration of the retinal backbone has only a small effect on the torsional mode progression and consequently on the movement of the ground and excited electronic states towards the CI, because the torsion is predominantly localized on the carbon framework.24,43 Since the surface hopping probability is directly linked to the evolution of this torsion to values close to 90 degrees, no significant kinetic changes are expected upon deuteration in agreement with our experimental and theoretical observation of a weak isotope-dependence on the excited-state lifetime. The main difference between the isotopomers used here is that the C11-H and C12-H wags are coupled for native 11,12-H2 rhodopsin and for 11,12-D2, resulting in the
formation of symmetric and anti-symmetric HOOP vibrations where the two hydrogen (deuterium) displacements maintain a specific phase relationship with the carbon torsional coordinate until the molecule decays via the CI. In this context, di-deuteration provides a slightly more suitable phase-matching of the HOOP to the torsional motion, resulting in an increase in the isomerization quantum yield (compare Supplementary Fig. 12 and 13). When a single position is deuterated, however, that coupling is reduced resulting in more isolated C-H and C-D out-of-plane wags associated with a less well-phased HOOP motion.44 Consequently, a single deuteration significantly alters the phase relationship between the C-H and C-D wagging motions and ultimately the torsion at the CI, thereby inhibiting photoproduct formation.
Two-mode harmonic model
To understand how an increasing level of deuteration of the C11=C12 double bond can result in the observed non-monotonous quantum yield trend (increase for 11,12-D2, decrease for 11-D and 12-D) for the vibrationally coherent photoisomerization in rhodopsin, we constructed a minimal two-mode harmonic model with frequency parameters (ωα and ωδop) derived from the simulations (see Supplementary Information, section 7). The model contains a torsional mode with ωα = 83 cm-1 and a HOOP mode with an isotope-dependent ωδop = 953 cm-1, 855 cm-1 or 725 cm-1 for 11,12-H2, 11-D/12-D or 11,12-D2, defined by equations (1) and (2).
α = 𝐴α𝑐𝑜𝑠[𝜔α𝑡] + 𝐵 (1)
δop= 𝐴δop𝑐𝑜𝑠[𝜔δop𝑡 + 𝐶] (2)
The amplitude parameters Aα and Aδop are also extracted from the 400 calculated trajectories and kept constant in all cases. The B and C coefficients represent initial conditions (t = 0) and are obtained from the simulated Boltzmann distribution of each isotopomer. Each trajectory computed using equations (1) and (2) represents the coherent dynamics of a population subset defined by the B and C values.
The modeled time evolution of α, δop and the resulting τ value for specific B and C values of the 11,12-H2
isotopomer are illustrated in Fig. 5a. The normalized fraction of decayed trajectories at each time point is calculated to be proportional to the velocity of τ multiplied by the value of a reference Gaussian function (derived from the simulations) and a population decay factor, which represents the decay probability (Fig.
5a, gray shaded area). The population subset of 11,12-H2 decays in three distinct waves (Fig. 5a, bottom), namely two reactive (orange) and one unreactive (blue) wave, showing the same oscillatory character of the population decay found in the full simulation (Fig. 4b). In fact, the short time separation between the first reactive and the unreactive wave and the larger time separation between the two successive reactive waves in Fig. 5a roughly matches the time separations between the corresponding reactive and unreactive maxima found in the simulation (Fig. 4b). These observations indicate that the oscillations in the population decay for both the reactive and unreactive sub-populations are present in a basic 2D model and must results from the superposition of trajectory subsets with the same features but displaying decay waves at different times and amplitudes. The modeling of trajectories characterized by different B and C values and/or ωδop value indicates that the above conclusions are general.
The origin of the modeled decay waves can be understood by considering the corresponding temporal evolution of the torsion and HOOP coordinates (Fig. 5b). At ~70 fs delay (compare Fig. 5a and 5b), the trajectory enters the decay region. Initially the trajectory shows a positive velocity of δop and the corresponding decay leads to photoproduct formation (compare Fig. 5b to Fig. 4d). At the turning point, the trajectory inverts its direction still remaining in the decay region and thus leading to reactant formation upon decay. At ~85 fs, the trajectory exits the decay region halting a population decay. Just before 100 fs, however, the trajectory re-enters the decay region with a positive velocity of δop leading to a second wave of photoproduct formation, which is stopped after ~110 fs.
According to the above model the change in the overall quantum yield upon isotopic labeling depends on three factors characterizing each population subset: the initial conditions, the evolution of the phase relationship between δop and α and the magnitude of the dephasing of the C11-H and C12-H wags. We find that the deviation of the average δop of the simulated trajectories, d(δopAV)/dt, of asymmetrically deuterated
isotopomers is more sensitive to the value of the initial conditions than that of their symmetric counterparts.
This is reflected by the deviation of the simulated population dynamics from a trajectory released from the Franck-Condon point with no velocities (see Supplementary Fig. 12). More specifically, the 11,12-H2 and 11,12-D2 populations follow rather closely such trajectory revealing that the corresponding motion is dominated by the structure of the excited-state potential energy surface rather than by the initial velocities.
This condition would guarantee a high degree of vibrational coherence. In contrast, the 11-D and 12-D populations display much larger deviations suggesting a more de-phased motion and a lesser degree of vibrational coherence. Thus, despite being intrinsically dependent on a frequency change occurring upon isotopic substitution, the observed/simulated isotope effect should be described as a vibrational phase isotope effect, since it relies on the dynamic phase relationship achieved at the CI by the fundamental vibrational modes involved in the reaction coordinate. It is thus distinctly different from the often-employed primary and secondary kinetic isotope effects, which operate after dephasing has taken place.
Conclusion
We have shown experimentally and theoretically that deuteration along the isomerizing double-bond of the retinal chromophore in rhodopsin causes a significant and unanticipated pattern of isomerization quantum yield changes while inducing only modest perturbations of the kinetics in line with known isotope effects.
The lack of correlation between these two experimental observables points towards the existence of a novel vibrational phase isotope effect that could be functionally important for other ultrafast and vibrationally coherent processes.45 Although illustrated here for rhodopsin photochemistry, vibrational phase isotope effects should be a general and powerful approach for revealing the importance of vibronic coupling in ultrafast light induced processes, such as Förster or Dexter energy transfer, electron transfer, ultrafast internal conversion or proton transfers. The fact that this vibrational phase isotope effect is manifested in the quantum yield measured with incoherent light demonstrates the importance of intramolecular multimode vibrational coherence in photochemical reactions, irrespective of the illumination conditions.40,41 Finally, we remark that the observed phase dependence is most likely not only a classical effect but intrinsically linked to the quantum nature of the reaction in a non-adiabatic region of the potential energy
surface. In rhodopsin, the vibrational phase modulations affecting the quantum yield also have an impact on the electron re-coupling, a purely quantum mechanical process, which allows for the C11=C12 double bond reconstitution. The vibrational isotope effect thus opens new avenues for studying ultrafast energy flow in vibronic processes beyond the Born-Oppenheimer approximation.
Acknowledgments
We acknowledge support from the National Eye Institute for providing 11-cis retinal used to make the 11,12- H2 regenerated rhodopsin sample. P.K. was supported by the EPSRC (EP/K006630/1). M.O. is supported by the NSF (CHE-1710191) and HFSP (RGP0049/2012) and also thanks the Ohio Supercomputer Center for computer time. I.S. is supported by the ERC Starting Grant ‘PhotoMutant’ (678169). This work was supported in part by the Mathies Royalty Fund.
Author Contributions
R.A.M. and J.L. conceived the project. P.K., C.S. and M.L. designed all experiments and analyzed the data. J.L.
and I.F. synthesized the isotopomers. M.O. and X.Y. carried out the molecular dynamics simulations and developed the proposed theoretical model. I.S. and A.V. wrote the isotope simulation code. K.M.S. prepared the rhodopsin samples for all measurements. C.S., P.K., M.O. and R.A.M. wrote the manuscript with contributions from all other authors.
Competing financial interests
The authors declare no competing financial interests.
Corresponding authors
*ramathies@berkeley.edu; philipp.kukura@chem.ox.ac.uk; massimo.olivucci@unisi.it
Methods
Sample Preparation
Rhodopsin samples were prepared in a 100 mM sodium phosphate buffer (pH 7.1% Ammonyx-LO) as described by Eyring et al.44 with optical densities at 498 nm of: OD(native rhodopsin) = 3.0, OD(11,12-H2
regenerated) = 3.4, OD(11,12-D2) = 4.2, OD(11-D) = 0.54, OD(12-D) = 1.3.
Ultrafast Spectroscopy
The experimental setup has been described by Liebel et al.36 Briefly, pulses were delivered by a Pharos-6W amplifier system (LightConversion, 1030 nm, 180 fs, 1.05 W at 1 kHz). A small fraction was split off to generate the white light probe pulses (500-900 nm) in a 3 mm sapphire crystal. Pump pulses were generated in a home-built non-collinear optical parametric amplifier as detailed elsewhere,46 and compressed to 20 fs (transform-limit) with a set of chirped mirrors (Layertec).
Samples were flowed through a 500 m path length flowcell (120 m windows) by a peristaltic pump at a rate sufficient to ensure replenishment of the sample between consecutive laser shots. Furthermore, we added NH2OH (0.2 mM) to degrade subsequent photointermediates. Pump and probe focus diameters were 65 and 44 m with corresponding pulse energies set to 20 nJ and 2.5 nJ, respectively. The optical densities of the samples at 500 nm in the sample cell were: OD(rhodopsin) = 0.15, OD(regenerated) = 0.17, OD(11,12- D2) = 0.21, OD(11-D) = 0.027, OD(12-D) = 0.065.
Quantum Yield Measurements
Continuous-wave laser output (532 nm, 0.6 mW) was passed through a Glan-Taylor polarizer (Thorlabs), narrow-band filtered (532 nm, FWHM = 10 nm, Thorlabs) and attenuated to 1 W before being split by a 50:50 beamsplitter (Thorlabs) into a reference and a sample beam. The sample beam illuminated a 1 cm path length quartz cuvette. Both reference and transmitted sample beams were subsequently detected with an EMCCD (Andor iXon3 860). Integration of the detected spots provided (referenced) bleaching curves (corrected for 4.5% back-reflection of the cuvette), which were analyzed using the established protocol.33,34
Samples were diluted with buffer solution (100 mM sodium phosphate buffer, pH 7.1% Ammonyx-LO) to an OD at 498 nm of 0.3 and NH2OH was added to rapidly degrade later photointermediates. Each sample was stirred constantly during the measurement and illuminated for 20 min corresponding to a bleaching of <15
% of the initial molecules. The quantum yield of the 11-cis chromophore in methanol was measured according to the procedure described by Sovdat et al.37,47
Statistical significance (n=4) was determined based on a t-test at 99% confidence interval to yield p(11,12-H2
regenerated)=0.111, t(11,12-H2 regenerated)=1.867; p(11,12-D2)=6.9x10-4, t(11,12-D2)=9.694; p(11-D)<1x10-
5, t(11-D)=27.014; p(12-D)=2.8x10-5, t(12-D)=11.342.
Simulations
The employed QM/MM model was constructed starting from the 2.2 Å resolution crystallographic structure of bovine rhodopsin (PDB code: 1U19)48 and following the protocol reported by Luk et al.49 All retinylidene, NH and CεH3 atoms linked to the Cδ atom of the Lys296 side-chain were included in the QM subsystem. The remaining atoms formed an MM subsystem described by the AMBER94 force field.50 After QM/MM geometry optimization at the CASSCF(12,12)/6-31G*/Amber level, a more computationally affordable model featuring a chromophore with five conjugating double bonds was generated following the protocol described by Manathunga et al.51 and geometrically optimized at the CASSCF(10,10)/6-31G*/Amber level. This model was then used to simulate a room-temperature Boltzmann-like distribution and extract 400 initial conditions for each isotopomer at room temperature.51 Finally non-adiabatic population dynamics at the same CASSCF(10,10)/6-31G*/Amber level were performed using the stochastic Tully surface-hop method.52,53 All calculation were run using the Molcas54/Tinker55 interface suitably modified to account for the deuterium mass. More details are provided in the Supplementary Information, sections 4-7.
Data availability
The authors declare that the data supporting the findings of this study are available within the main article and the Supplementary Information. Additional data are available from the corresponding author upon request or can be accessed free of charge at http://ora.ox.ac.uk.
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Figure captions
Figure 1. Native and isotopically labelled 11-cis retinal protonated Schiff base chromophores in rhodopsin studied in this work.
Figure 2. Isomerization quantum yields for native, 11,12-H2 regenerated and isotopically labelled retinal chromophores in rhodopsin obtained at an excitation wavelength of 532 nm. Grey - symmetrically substituted, orange - asymmetrically substituted. The quantum yields are compared to the free chromophore in methanol solution (blue,*) obtained using a different procedure (see Methods).
Figure 3. Transient absorption measurements and corresponding fitting results of rhodopsin regenerated with retinal chromophores with different patterns of isotopic substitution about the isomerizing C11=C12
double bond. a, Normalized differential absorbance averaged over the full photoproduct absorption band (545-616 nm, grey circles) and corresponding fits (black dashed). The photoproduct rise has been highlighted in orange for clarity. Traces were normalized to the maximum absorption feature occurring at a time delay of 200 fs. Time delays <75 fs (grey shaded) have been manually scaled as indicated to show coherent artifact and photoproduct signal contributions on the same scale for visual purposes. b, Retrieved lag (or delay) time before photoproduct formation and c, Rise time of the photoproduct after the lag period. Error bars represent one standard deviation. See Supplementary Information, section 2, for detailed trace alignment and fitting procedure.
Figure 4. Simulated excited-state isomerization dynamics of bovine rhodopsin. a, Dihedral angles defining the chromophore double-bond torsion (α) and hydrogen-out-of-plane (δop) coordinates. The relationship between the ‘overlap’ coordinate (τ) and the π-orbitals (green) responsible for double bond reconstitution is schematically illustrated on the right. hδop(H11) is defined as the dihedral angle between the H11C11C12 and
C10C11C12 planes and hδop(H12) is defined as the dihedral angle between the H12C11C12 and C11C12C13 planes in such a way that the relationship δop = hδop(H11) + hδop(H12) is satisfied. b, Oscillatory character of the excited- state population decay for both the reactive and unreactive sub-populations. c, Distribution of the τ velocities at the decay point (CI) for the reactive and unreactive sub-populations. Negative and positive τ velocities correlate with reactive (orange) and unreactive (blue) events, respectively. d, Representative reactive and unreactive trajectories showing that the sign of the τ velocity is determined by the sign of the δop velocity.
The two straight dashed lines give the corresponding values of τ for the reactive (orange) and unreactive (blue) trajectory.
Figure 5. 2D-modeling of simulated rhodopsin population dynamics. a, Graphical representation of the α and δop periodic functions and Gaussian decay region defining the model. The alternating reactive and nonreactive population decay events produced by the model are projected below. b, Origin of the reactive (orange) and nonreactive (blue) decay events in terms of trajectory segments characterized by an increase and decrease of δop while α is monotonically increasing. The shaded area between τ = -76 and τ = -96 degrees defines the decay region (gray shaded) centered along the collection of CI points forming the intersection space (black dashed line).15
Tables
Table 1. Comparison of experimental and simulated photoproduct kinetics and quantum yields for rhodopsin isotopomers. All indicated errors refer to one standard deviation.
11,12-H22 11,12-D2 11-D 12-D
Experiment lag time1 (fs) 147.7 ± 1.0 156.8 ± 1.9 155.0 ± 0.86 148.8 ± 1.1 quantum yield 0.63 ± 0.01 0.69 ± 0.01 0.45 ± 0.02 0.48 ± 0.01 Simulation hop time3 (fs) 100 ± 31 113 ± 41 100 ± 35 93 ± 35
quantum yield 0.69 0.70 0.61 0.58
1Lag time (t0,PIA - t0,CA) derived from non-linear fit (see Supplementary Information, section 2). 2Experimental values for native rhodopsin. 3Average hop time.
